Tamoxifen has been found to reduce the incidence of breast cancer in women at increased risk, but has some troublesome side effects. It is FDA-approved for this indication. Raloxifene has been FDA-approved for the prevention of osteoporosis. Raloxifene may also reduce the risk of devloping breast cancer with fewer side effects than tamoxifen. This randomized, double-blind study will determine if raloxifene is either more or less effective than tamoxifen in reducing the incidence of invasive breast cancer in postmenopausal women who are at increased risk for the disease. A secondary goal is to determine whether raloxifene reduces the endometrial cancer rate as compared to tamoxifen.